Non-Gaussianity: Comparing wavelet and Fourier based methods

¹ IAS-CNRS, Bâtiment 121, Université Paris Sud, 91405 Orsay Cedex, France
² Denys Wilkinson building, Oxford University, OX1 3RH, Oxford, UK
³ Astronomy Centre, University of Sussex, BN1 9QJ, Brighton, UK

Corresponding author: N. Aghanim, Nabila.Aghanim@ias.u-psud.fr

Received: 10 January 2003
Accepted: 28 April 2003

Abstract

In the context of the present and future Cosmic Microwave Background (CMB) experiments, going beyond the information provided by the power spectrum has become necessary in order to tightly constrain the cosmological model. The non-Gaussian signatures in the CMB represent a very promising tool to probe the early universe and the structure formation epoch. We present the results of a comparison between two families of non-Gaussian estimators: The first act on the wavelet space (skewness and excess kurtosis of the wavelet coefficients) and the second group on the Fourier space (bi- and trispectrum). We compare the relative sensitivities of these estimators by applying them to three different data sets meant to reproduce the majority of possible non-Gaussian contributions to the CMB. We find that the skewness in the wavelet space is slightly more sensitive than the bispectrum. For the four point estimators, we find that the excess kurtosis of the wavelet coefficients has very similar capabilities than the diagonal trispectrum while a near-diagonal trispectrum seems to be less sensitive to non-Gaussian signatures.